I didn't post this in the science section because I wanted to find out more about how they relate to the Big Five, MBTI Step II and MBTI Step III. I am a "lay person" when it comes to these things but quite statistically savvy. It may sound arrogant, but I believe I understand common factor analysis, principle component analysis, other factor models, and multivariate linear regression in general, better than most people--even many who (over)use it regularly.

This is what I do know(I'll be doing a lot of "explaining," not to be condescending, but simply to get people who may be interested up to speed).

There are two kinds of distributions that seem to come up in this forum:

- "bimodal" distributions. Bi-modal meaning "having two modes." Mathematically speaking the
modeof a distribution is the most frequently occurring value in the distribution--the "peak" if you will. A bimodal distribution will show two peaks. Granted, one may be the official mode, mathematically speaking. But plotting the distribution visually will show to peaks.

This kind of distribution, I believe, is popular in the Myers-Briggs and related typologies. I have no idea what particular bimodal distributions are used for each dichotomy, but I suspect the sum of two Gaussians of different means is popular.- "Gaussian" distributions. Also, called "bell curves," or "normal" distributions. I dislike the use of the word "normal" because, in my training, that is reserved for the Gaussian of mean 0, and standard deviation of 1. Also, words like "normalize" are used for distributions of all sorts, so it can create confusion in the belief that when we "normalize" something we are trying to force fit something to a Gaussian (which may or may not be true).

Gaussians are the kinds of distributions seen in the Five Factor Model typology, I believe.

Some facts that I believe everyone participating in the discussion should know

- The most important statistical fact (beyond the Law of Large numbers which people seem to know inherently) I believe people should know is the
Central Limit Theorem.

The Central limit theorem states that the sum of independent, identically distributed random variables of finite variance tends towards a Gaussian distribution. It should be clear to people that the same is true for averages of identically distributed random variables (simply scaled down by the number of variables added together).

The relevance here is that if you have a big questionnaire in which all the questions have bimodal distributions in the answers, the sum or average will tend to be Gaussian, unless there is a strong correlation between the answers given on each of the questions. This seems to be an artifact of testing also. In a way, you can create "noise" in a test which when added together tends to be Gaussian (this is especially true if the noise is purely random).- A psychological tendency know as the
Central Tendency Bias. When given a range of selections to chose from, people tend to chose toward the middle, even if a more extremal value is more accurate. When it comes to answering questions describing our own personalities, this will also tend to create a more Gaussian distribution.- The distribution of answers on a question with only two answers will necessarily be bimodal because there are only two possible values. That is Bivalent implies bimodal. This seems to be an artifact of how the question is asked, not necessarily anything real.

My questions in general concerning the "validity" of personality systems

- Why we believe that Step III will be more valid than the current MBTI?
- Why is the FFM more "academically blessed?"
- Why are MBTI, DiSC, Temperament (all Myers-Briggs like), etc. more popular in corporations still?
- Do you believe the use of either typologies leads to Self-fulfilling prophecies?
- Do you believe use of either typology will do more harm than good?
- Although, I understand the statistics behind various factor analysis, I find psychometric papers hard to read, because of assumed knowledge of what particular letter-denoted variables are, and general use of psychometric jargon. Is there a good way to find out what factor models are being used, and what the original data sets, correlation matrices, or covariance matrices were?